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Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students' opportunities to struggle, have been consistently linked to improving students' mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of professional development (PD) offerings. We describe three examples of how the framework is used to support teacher learning and classroom instructional practice: a state-mandated course, lesson studies, and a large-scale teacher-researcher alliance. Initial findings suggest that consistently emphasizing this framework provides both content and structural guidance during PD development and gives coherence and focus to teachers' PD experiences.

Construct maps and related item type frameworks, which respectively describe and identify common patterns in student reasoning, provide teachers with tools to support instruction built upon students' intuitive thinking. We present a methodological approach--embedded within common assessment development processes--for developing such construct maps and item type frameworks which entails (1) articulating a construct map, (2) developing diagnostic item types, (3) comparing item type difficulties, and (4) modifying or providing evidence in support of the construct map. We present an example focused on students' proportional reasoning based on its centrality to mathematical success. The results further inform our construct map for students' proportional reasoning and provide a diagnostic item-type framework.

Research-based learning in taught courses develops the skills needed to judge knowledge sources and think critically in a post-truth world. In viewing research skills as threshold concepts, the paper argues that transforming a student cannot be a one-off event. Research capacity must build over a programme and this requires coherent research skill development and assessment that is progressive (ipsative). A study of five programmes each with a different design of research 'throughline' showed that such integrated research-based learning generates three challenges. Firstly, conceptualising the research skills and progression is not easy. Secondly, the accumulation and enrichment of research skills is not readily visible to students. Finally, providing a clear support system across the programme is not straightforward. The paper concludes that these challenges need to be addressed if the potential of research-based education to enable future citizens to interrogate populist claims and reject misinformation is to be realised.

This article illustrates an argument-based approach to presenting validity evidence for assessment items intended to measure a complex construct. Our focus is developing a measure of teachers' ability to analyze and respond to students' mathematical thinking for the purpose of program evaluation. Our validity argument consists of claims addressing connections between our item-development process and the theoretical model for the construct we are trying to measure: attentiveness. Evidence derived from theoretical arguments in conjunction with our multiphased item-development process is used to support the claims, including psychometric evidence of Rasch model fit and category ordering. Taken collectively, the evidence provides support for the claim that our selected-response items can measure increasing levels of attentiveness. More globally, our goal in presenting this work is to demonstrate how theoretical arguments and empirical evidence fit within an argument to support claims about how well a construct is represented, operationalized, and structured.

Doctoral scientists increasingly forge non-academic careers after completing the doctorate. Governments and industry in advanced economies welcome this trend, since it complements the "knowledge economy" vision that has come to dominate higher education globally. Knowledge economy stakeholders consider doctoral scientists to constitute particularly high-value human capital; primed to contribute to economic growth via the creation and application of scientific knowledge. Little is known, however, about doctoral scientists' awareness of, and attitudes towards, the knowledge economy. This paper reports a study of UK doctoral scientists, which reveals that they are aware of, but ideologically divided towards, the knowledge economy. The knowledge economy relates to their scientific motivations, values and aspirations in complex ways. Four moral positions emerge, ranging from "anti" to "pro" knowledge economy. We discuss the characteristics of each moral position, concluding with the need for doctoral scientists to adopt better informed and more flexible professional outlooks.

Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically manipulating the location of an integer multiplier--to press the scalar or functional relationship--on item difficulty and student solution strategies. We administered short-answer assessment forms to 473 students in grades 6-8 (approximate ages 11-14) and analyzed the data quantitatively with the Rasch model to examine item accessibility and qualitatively to examine student solution strategies. We found that manipulating the location of the integer multiplier encouraged students to make use of different aspects of proportional relationships without decreasing item accessibility. Implications for proportional reasoning curricular materials, instruction, and assessment are addressed.

We examined the impact of a state-mandated K-12 mathematics professional development course on knowledge, self-efficacy, and beliefs of nearly 4,000 teachers and administrators. Participants completed the Mathematical Thinking for Instruction course, emphasizing student thinking, problem-solving, and content knowledge specific to mathematics instruction. Inventories utilizing items from the Learning Mathematics for Teaching project measured changes in participants' Mathematical Knowledge for Teaching (MKT) and an end-of-course self-evaluation enabled analysis of changes self-efficacy and beliefs. Statistically significant changes were found in all three variables. This study adds to our understanding of the potential usefulness of mandating large-scale professional development as a policy vehicle for influencing educators' mathematics knowledge and beliefs.

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so. Instead, these students tend to represent the physical characteristics of the situation. In addition, we discovered that middle-school students had sophisticated ideas of dependency and covariance. All the students were able to use their models of the situation to generalize and make predictions. These findings suggest that secondary students have the ability to describe covariant and dependent relations and that their models of functions tend to be more intuitive than mathematical--even for the students in algebra II and calculus. Our work suggests a possible framework that begins describing a way of analyzing students' understanding of functions.

This paper considers feedback in the context of modularised programmes in higher education in the UK. It is argued that the self-contained nature of modular assessment may limit feedback dialogue between staff and students to assignment-specific issues, and may impede student progress towards holistic programme-level aims and outcomes. A feedback profiling tool was developed to categorise feedback on draft and final work. The analysis of feedback on 63 samples of draft work and 154 samples of final work showed different patterns. There were more feedback comments on draft work, and the feedback comments were dominated by advice and critique, while the feedback comments on the final work were overwhelmingly dominated by praise. This pattern of feedback is problematised in terms of feed forward from one module to the next, as students work towards the development of programme-level outcomes. Ipsative feedback (on progress) and feed forward in terms of disciplinary-specific skills and programme-level outcomes are recommended to enable students to act on feedback on end-of-module work, and develop students' capacity to recontextualise disciplinary-specific skills throughout a programme. Some developmental applications for the feedback profiling tool are also suggested.

Distance learners often rely on written feedback for learning and for motivation. But feedback that is "given" to learners and that relies on praise to motivate does not engage learners in the process of self-development. We propose that an ipsative approach to assessment and feedback based on a comparison with a learner's previous performance motivates distance learners by developing a self-awareness of progress that encourages learners to interact with feedback and apply this to future work. A study of a distance learning Masters programme in Educational Leadership indicated that formal self-referential (ipsative) feedback was largely absent. An ipsative feedback scheme was therefore developed in consultation with the tutors in which students completed a reflection on their progress in implementing past feedback. Tutors provided both an ipsative and a developmental response. Student and tutor evaluations of the scheme indicated that feedback on progress has the potential to motivate distance learners and to encourage them to act on developmental feedback, but can also raise grade expectations. Sustainable methods of applying ipsative feedback to a wide range of distance learning programmes are worth further exploration.

The central role that assessment plays is recognised in higher education, in particular how formative feedback guides learning. A model for effective feedback practice is used to argue that, in current schemes, formative feedback is often not usable because it is strongly linked to external criteria and standards, rather than to the processes of learning. By contrast, ipsative feedback, which is based on a comparison with the learner's previous performance and linked to long-term progress, is likely to be usable and may have additional motivational effects. After recommending a move towards ipsative formative assessment, a further step would be ipsative grading. However, such a radical shift towards a fully ipsative regime might pose new problems and these are discussed. The article explores a compromise of a combined assessment regime. The rewards for learners are potentially high, and the article concludes that ipsative assessment is well worth further investigation. (Contains 2 figures.)

Collaborative learning has much to offer but not all learners participate fully and peer groups can be exclusive. The article examines how belonging or "congruence" in learning groups is related to identities of gender, age, ethnicity and socio-economic status. A study of student experiences of collaborative learning on three different blended learning courses illustrated how learners negotiate identity congruence with peer groups to belong and engage. An analytical framework that distinguishes social, operational and knowledge-related identity congruence has emerged. Contrary to received wisdom, the social aspect appears least important for learner engagement while knowledge-related identity congruence is fundamental. Some of the consequences of identity incongruence, particularly concerning gender and maturity, are discussed and the article points towards the pedagogies which might enable identities of group members to shift so that collaborative learning can flourish.

Enthusiasts for new social software do not always acknowledge that belonging to e-learning communities depends upon complex and often unresolved identity issues for learners. Drawing on the author's previous research on belonging in social learning, the paper presents a theory of identity congruence in social learning and brings to the foreground the importance of identities which arise from expressions of gender, class, ethnicity, age, etc. in the social, operational and, in particular, the knowledge-building aspects of learning. These three dimensions of identity congruence are used to evaluate the potential of new social software. While social software might encourage some learners to engage in social and operational identity work, there are disadvantages for others, and learner-generated knowledge and e-assessment practices can be divisive. Inclusive e-learning depends upon pedagogies and assessments which enable learners to shift and transform identities, and not solely on widening the range of technologies available. Such caution should underpin future research.

The history of educational development is rooted in the improvement of teaching techniques. As a result, centres or units have normally been located in central registrars or human resources departments, library, learning and technical support services, or established as semi-autonomous entities. The alignment of educational development with research at a teaching-led UK university marks a radical departure from these established patterns. The paper will explore some principles for the development of synergy between teaching and research through presenting the conceptual and strategic case for locating educational development in a university-wide Graduate School. This includes institutional commitment to renewing research capacity and the acceptance of a holistic model of academic practice and re-shaping of academic identity through strengthening the links between research and teaching via professional development. Three different approaches to bridging the cultural gap between teaching and research are compared and illustrated with examples from this case study.

It is often assumed that online collaborative learning is inclusive of diversity. In this exploratory paper, I challenge this notion by developing a theory which proposes that inclusion occurs through congruence between learners' social identities and the identities implicitly supported through the interactions in a particular community. To build identity congruence, e-learning communities need spaces for both commonality and diversity, and I present three paradoxes which underlie the aims of online learners and teachers to embrace diversity online. I illustrate these with some examples from online learning and teaching. The ability to "listen" to each other online offers a way forward, and the paper ends with some future possibilities about how we can ensure that e-learning communities benefit from diversity.